The properties of tar will not change in a vacuum (depending on how strong is the vacuum).

Some glues are air drying, but pine tar is not. The adhesion and cohesion properties do not change with oxygen or gravity.

However, pine tar is a mixture of hydrocarbons, acids and bases. At low vapour pressure some of those will evaporate / outgas. All the volatile stuff is acting as a solvent for the non-volatile stuff. Too strong a vacuum or too long in vacuum and the pine tar will become hard and brittle.

Problems exist in space because of the vacuum but also it's really cold. Many adhesives are only active above the glass transition temperature or melting point.

There are test standards for minimal outgassing required for adhesives used in space craft. It must not lose too much mass, and that lost mass should not recondense in a harmful way.